Analysis Of "Linear Function" Critical Learning Path Based On Knowledge Space Theory And Concept Map

Function is the focus and difficulty of mathematics teaching in junior high school,and the linear function is the first specific function that students are exposed to,which is closely related to numbers and formulas,equations and inequalities,and is also the basis for subsequent learning of inverse proportional function and quadratic function.Knowledge Space Theory,as a cognitive diagnostic method to deeply understand students’ learning,effectively solves the problem that traditional tests only emphasize the results of behavior and the products of mental activities,and lack attention to the internal processes that produce these results or products.Diagnostic learning path can help teachers achieve professional development,improve the level of mathematics teaching,and can realize the mutual promotion of students’ individual development and class social development,and help teachers understand students’ thinking and dig deep into the connotation of knowledge.Based on the knowledge space theory,it is of great significance to study the key learning paths of students’ "linear function" chapter.So,on the basis of knowledge space theory,the paper analyzes the key learning paths of "linear function" of eighth grade students,and studies the cognitive characteristics of the super and the lower students with the help of concept maps.In order to obtain the key learning paths for all students,the super students and the lower students,with reference to the Compulsory Education Mathematics Curriculum Standards(2022 Edition)and Compulsory Education Textbook Mathematics(Grade 8)(Jiangsu Phoenix Science and Technology Press),the four subsections of the "Linear Function" chapter,namely "Function","Linear Function","Image of Linear Function" and "Solving Problems with Linear Function",were determined.On the basis of reading a large number of literature,based on the detailed list of knowledge points,we ensured that one knowledge point corresponds to a topic and examined a knowledge point one by one,and discussed and compiled the "linear function" test paper with middle school teachers and college professors.Correct the collected "linear function" test paper,register each student’s answer to each question in Excel software,use the KST statistical program independently developed based on Python language to process the collected data,and finally obtain the knowledge space diagram,all knowledge states and the probability corresponding to each knowledge state,according to which the key learning path is obtained.Compare the key learning paths preset by all students and experts to determine whether there are differences.In order to deeply understand the formation process and cognitive misunderstanding of the key learning paths of excellent students and poor students,the concept map questionnaire of "linear function" was compiled based on the course standard,Suke textbook and reference to existing literature.By analyzing the concept map of students corresponding to the knowledge state of each node in the key learning path,the cognitive characteristics and misunderstandings of the super students and the lower students in the "linear function" chapter can be obtained.After analyzing the key learning paths of all students,the super students and the lower students.it can be found that in the four subsections of the "linear function",the number of knowledge states existing at the same time of all students is large,the connection between knowledge states is complex,and they have large cognitive differences.In the three sections "Function"."Image of Linear Function" and "Solving Problems with Linear Function",there are certain differences between the key learning paths preset by all students and experts.In the "Linear Function" section,all students are exactly aligned with the key learning paths preset by the experts.In the three subsections of "Function","Linear Function" and "Image of Linear Function",the number of knowledge states existing at the same time of the super students is small,the connection between knowledge states is clear,and their cognitive states are relatively consistent.In the section "Solving Problems with Linear Function",the number of knowledge states existing at the same time of the super students is large,and the connections between knowledge states are complex,and they have large cognitive differences.In the three subsections of "Function"."Linear Function" and"Image of Linear Function",the number of knowledge states existing at the same time of the lower students is large,and the connection between knowledge states is complex,and they have large cognitive differences.In the section "Solving Problems with Linear Function",the number of knowledge states that exist at the same time of the lower students is small,the connections between knowledge states are clear,and their cognitive states are relatively consistent.For nodes at the end of the critical learning path,instructors can take some remedial and preventive actions.Analyzing the concept map questionnaire and test paper,it is concluded that there are three major problems in the learning of knowledge points:"lack of awareness of applying the knowledge learned","difficulty in forming a systematic knowledge system" and"concept does not form an object entity",and corresponding suggestions are made accordingly.In addition to the teaching of knowledge points,the author also suggests that teachers should pay attention to mathematical operation training,improve students’ mathematical operation ability,pay attention to mathematical language translation,and enhance students’ awareness of number and form combination.